Method for simulating streamer positioning, and for navigation aid

ABSTRACT

The invention relates to a method of simulating the positioning of a streamer towed by a ship ( 10 ) during an operation of acquiring geophysical data at sea, said acquisition operation making use of shots from at least one sound source (Sa), the method implementing a hydrodynamic model of the interaction between marine current, the path of the ship, and the streamer, the method being characterized in that it includes determining variations in the current over time and in space. The invention also relates to a method of assisting navigation for a seismic survey ship, and to a method of predicting coverage fraction by implementing such a simulation method.

[0001] The invention relates in general to operations performed at seafor acquiring geophysical data by means of a ship towing one or morecables associated with hydrophones.

[0002] More precisely, the invention relates to a method enabling thedeformation of the cables towed by a ship to be predicted effectively,and it enables advantage to be taken of such prediction.

[0003] The purpose of geophysics is to describe the structure of thesubsoil. The technique in widest use is reflection seismic surveying.When surveying off-shore, the principle is to emit a high power soundpulse towards the subsoil; the sound wave created in this way isreflected partially at the interfaces between the successive geologicallayers it encounters, and it returns towards the surface wherehydrophones transform the sound signal into electrical signals.

[0004] In off-shore surveying, the sound source is generally constitutedby air guns, and the hydrophones are grouped together in groups whichare integrated in cables known as “streamers” that are towed by theship.

[0005] The number of sound sources and streamers, and the lengths of thestreamers can be varied. Depending on required resolution, the distancebetween two consecutive groups varies over the range 12.5 meters (m) to25 m. A simple configuration having two streamers S1 and S2, a singlesound source Sa, and a plurality of groups T is shown in FIG. 1.

[0006] This figure also shows the so-called “common midpoints” (CMPs)that, for each {source, group} pair correspond to the subsurface pointof reflection.

[0007] In practice, interaction between sea currents and immersedstreamers gives rise to geometrical deformations in the systemconstituted by said streamers and the set of towed elements, therebycompromising the uniformity of coverage in the zone whose subsoil is tobe characterized. These deformations vary in time and give rise tocoverage “holes” which need to be filled in by additional passes of theboat, a process known as “infilling”.

[0008] This constitutes a major drawback since additional passesincrease the time required to perform operations and can give rise tovery significant increases in cost (which can be as much as 20%).

[0009] In addition, the extra time and cost associated with infillingcan vary very greatly from one operation to another, and it is thereforenot possible to predict them accurately, thus preventing operators fromgiving accurate predictions concerning the time and cost of a projectedoperation; this constitutes an additional drawback for operators.

[0010] It will thus be understood that there exists a manifest need toreduce infilling and also to predict the amount of infilling that willbe required in a projected data acquisition operation. In order tosatisfy these needs, it is necessary to characterize the influence ofcurrent on streamer deformation.

[0011] In this respect, attempts have been made to model the deformationof a streamer towed by a ship and subjected to current. For example,reference can be made to the article “The shape of a marine streamer ina cross-current” by P. P. Krail and H. Brysk, published in Vol. 54, No.3 of the journal of the Society of Exploitation Geophysicists.

[0012] However, such attempts do not reproduce real current conditions(the article mentioned assumes in particular that the current is steadyand the ship follows a uniform rectilinear path) and a result theresults thereof are unsuitable for being used directly so the abovedrawbacks remain.

[0013] The object of the invention is to enable those drawbacks to bereduced.

[0014] To achieve this object, the invention firstly provides a methodof simulating the positioning of a streamer towed by a ship during anoperation of acquiring geophysical data at sea, said acquisitionoperation making use of shots from at least one sound source, the methodimplementing a hydrodynamic model of the interaction between marinecurrent, the path of the ship, and the streamer, the method beingcharacterized in that it includes determining variations in the currentover time and in space.

[0015] Other preferred, but non-limiting features of the method of theinvention for simulating the positioning of a streamer are as follows:

[0016] the method comprises:

[0017] receiving primary current values as measured and/or predicted;

[0018] defining vector fields or ‘current objects’ of respective typescorresponding to different representations of the current and built upfrom said primary current values; and

[0019] selecting a ‘current object’ as a function of the intendedapplication;

[0020] ‘current object’ selection takes account of proximity in timebetween the instant for which the prediction is made and the instant atwhich prediction is performed;

[0021] ‘current object’ selection takes account of correlation betweenearlier ‘current object’ predictions and measurements of currentperformed at the instants for which said earlier predictions were made;

[0022] the coordinates of at least some ‘current objects’ comprisevalues measured on site;

[0023] the coordinates of at least some ‘current objects’ compriseextrapolated values predicting current;

[0024] some ‘current objects’ are computed by using a predictor filterenabling a current data series to be extrapolated from measurements ofcurrent made in the acquisition zone;

[0025] the defined types of ‘current object’ comprise the followingtypes:

[0026] 1) total current as measured by a current meter;

[0027] 2) tidal current as derived from meteorological bulletins, or asdeduced from measurements of current by harmonic analysis;

[0028] 3) the sum of a tidal current plus a residual current, said tidalcurrent being derived from meteorological bulletins or being deducedfrom measurements of current by harmonic analysis, and said residualcurrent being taken from meteorological bulletins;

[0029] 4) an extrapolation from total current as measured by a currentmeter;

[0030] 5) the sum of a tidal current and a computed residual current,said tidal current being taken from meteorological bulletins or beingdeduced from measurements of current by harmonic analysis, and saidresidual current being obtained by subtracting said tidal current fromthe current measured in the acquisition zone;

[0031] 6) a history of past extrapolations of the total current asmeasured by a current meter; and

[0032] 7) the sum of a tidal current and a history of pastextrapolations of a series of values constituted by the total current asmeasured by a current meter from which a tidal current has beensubtracted, said tidal current being taken from meteorological bulletinsor being deduced from measurements of current by harmonic analysis;

[0033] while computing ‘current objects’ of types 4, 5, 6, or 7, theprocessed data series is considered as a second order non-centeredsteady random process;

[0034] while computing values of a ‘current object’ of type 4, 5, 6, or7, weights are given to the measurements of the data series forextrapolation, which weights are inversely proportional to their age,for the purpose of anticipating sudden changes due to the residualcurrent;

[0035] while computing a particular value of a ‘current object’ of type4, 5, 6, or 7, a variance function of the difference between thepredicted value and the exact value of the current or the residualcurrent at the instant for which the prediction was computed isminimized, where said variance function has the form:$G = {\left( {1 - 1 - {\sum\limits_{i = 3}^{P + 1}{a_{i}a_{3}\quad \cdots \quad a_{p + 1}}}} \right){\Gamma_{U}\begin{pmatrix}1 \\{{- 1} - {\sum\limits_{i = 3}^{P + 1}a_{i}}} \\a_{3} \\\vdots \\a_{P + 1}\end{pmatrix}}}$

[0036] while computing a particular value of a ‘current object’ of type4, 5, 6, or 7, an autocorrelation function of the current or residualcurrent data series is computed, and then a linear system of equationsis set up and solved;

[0037] while computing a particular value of a ‘current object’ of type4, 5, 6, or 7, the linear system to be solved is conditioned byimplementing a descent method, preferably the conjugate gradient method;

[0038] the method provides the option of computing extrapolated valueson a series of measured current values from which a tidal current haspreviously been subtracted so as to compute an extrapolated residualcurrent, and then adding the tidal current corresponding to the instantfor which the extrapolation has been made to said extrapolated residualcurrent;

[0039] the method comprises estimating the performance of differentpredictions of current by comparison with a measurement of currentperformed at the time corresponding to the time of the predictions;

[0040] the method comprising estimating the performance of a ‘currentobject’ derived from predictions and/or measurements of current bycomparing the measured streamer positioning and the simulated streamerpositioning, said simulation taking account of the ‘current object’whose performance is to be estimated; and

[0041] the performance of the ‘current object’ is described by criteriawhich comprise the average of the absolute value of the differencebetween measurement and simulation of streamer positioning, and/or thedifference between predicted and measured streamer positioning below thevalue for which 90% of the prediction points are to be found.

[0042] The invention also provides a method of assisting the navigationof a ship towing at least one streamer in order to reduce zones ofundercoverage and/or overcoverage generated during a geophysical dataacquisition operation at sea during which the ship travels along aplurality of lines extending in a general direction defining an abscissaand forming an array covering a desired zone, the method beingcharacterized in that it implements a method of simulating streamerpositioning according to any of the above-mentioned features.

[0043] Preferred but non-limiting features of the method of theinvention for assisting navigation are as follows:

[0044] it comprises determining the set of {ship position; instant}pairs at regular intervals in space so as to define a track along whichthe orientation of the streamer at a given abscissa along the generalorientation of the lines of the array is as close as possible to theorientation of an associated streamer during a previous pass of the shipalong an adjacent line;

[0045] the method comprises the following steps:

[0046] selecting a ‘current object’ of appropriate type;

[0047] defining optimization parameters;

[0048] computing the positioning of a ‘reference streamer’ from datarelating to the streamer positioning of the adjacent profile and theoptimization parameters;

[0049] taking account of ship speed and direction data and streamerpositioning data at the time optimization computation is started;

[0050] creating a three-dimensional optimization grid with a firstdimension (Y) parallel to said general direction, a second direction (X)being perpendicular to the general direction, and included in thehorizontal plane, and the third dimension (DT) representing possibletime increments between two nodes spaced apart by one grid cell in thegeneral direction (Y);

[0051] simulating variations in the positioning of the streamer towed bya ship following all of the tracks defined by the nodes of theoptimization grid;

[0052] for all of the possible tracks, computing a norm of thedifference between simulated streamer positioning and reference streamerpositioning; and

[0053] computing an optimum track for which the associated norm is aminimum;

[0054] the optimization step comprises minimizing a norm of thedifference between reference streamer positioning and simulated streamerpositioning;

[0055] said normal to be minimized has the form:${H\left( {{X1},{\delta \quad {t1}}} \right)} = {{\sum\limits_{j = 1}^{J}\sum\limits_{k = 1}^{K}}{{{X_{reference}\left( {k,j} \right)} - {X_{predicted}\left( {k,j} \right)}}{f(k)}}}$

[0056]  where:

[0057] X1 is a series of J consecutive values for the position of thestreamer head along the horizontal direction of the optimization gridperpendicular to the general direction;

[0058] δt1 is a series of J consecutive values for the duration taken bythe streamer head to pass form one node of the optimization grid ofcoordinates (X_(i1), Y_(j), δt_(k1)) to a node having coordinates(X_(i2), Y_(j+1), δt_(k2)),

[0059] J is the number of nodes of the grid in said general direction(Y);

[0060] K is the number of curvilinear abscissa points along thediscretized streamer;

[0061] X_(reference)(k, j) is the position along the X axis of the point“k” of the ‘reference streamer’ when the head thereof is at the jthplane of the optimization grid along the Y axis;

[0062] X_(predicted)(k, j) is the position along the X axis of the point“k” of the simulated streamer when the head thereof is at the jth planeof the optimization grid along the Y axis; and

[0063] f(k) is a weighting function applied to the difference betweenthe simulated streamer and the reference streamer;

[0064] the method implements an optimization criterion for saiddifference between the measured and predicted streamer-positioning data;and

[0065] the step of optimizing zone coverage is implemented in real timeso as to provide the ship with a series of {instant; ship position; shipspeed} triplets to follow so as to optimize the path of the ship along aline that the ship is surveying.

[0066] The invention also proposes an application of the method ofassisting navigation as outlined above, to determining a path and astarting time associated with a forthcoming line that is to be surveyedby the ship, and also for determining the best forthcoming line tosurvey. In this application, in a preferred feature, a line startingtime is sought from within a given time window that corresponds tominimizing undercoverage and overcoverage.

[0067] Finally, the invention provides a method of predicting thecoverage fraction associated with an operation of acquiring geophysicaldata that is to be performed at sea over a given zone, the method beingcharacterized in that it implements simulating the track of a shipincluding a method of assisting navigation as outlined above.

[0068] Other features, objects, and advantages of the invention willappear more clearly on reading the following description of a preferredbut non-limiting implementation of the invention given with reference tothe accompanying drawings in which, in addition to FIG. 1 describedabove in the introduction to this specification:

[0069]FIGS. 2a to 2 d are diagrams of a ship towing streamers inoperation and of the coverage zones generated by the passage of theship;

[0070]FIG. 3 shows the coverage achieved in a zone, and serves inparticular to show up the infill zones;

[0071]FIG. 4 is a block diagram showing the structure of a system forimplementing the invention;

[0072]FIGS. 5a to 5 d set out the various results of predictions ofcurrent implemented in the invention;

[0073]FIGS. 6 and 7 are of the block diagram type showing the currentprocessing and predicting of current as implemented in the invention;

[0074]FIG. 8 shows a grid covering a zone to be surveyed and thesuccessive paths of the ship over the grid, together with theorientation of a streamer towed by the ship;

[0075]FIGS. 9 and 10 are optimization diagrams implemented in themethods of the invention;

[0076]FIG. 11 is a diagram showing two pairs of adjacent profiles, oneof which is optimized for reducing the amount of infilling;

[0077]FIG. 12 is a graphical representation of a function to beminimized in the invention; and

[0078]FIG. 13 shows three different profiles of a performance criterionconcerning streamer drift prediction as implemented in a method of theinvention for assisting navigation.

[0079] With reference now to FIG. 2a, there can be seen a diagram of aship 10 traveling in the direction of an arrow F, along a path (alsoreferred to as a “line” or “profile”) Li. Two streamers S1 and S2 areshown diagrammatically behind the ship, each streamer carrying groups ofgeophysical sensors (not shown in the figure). These streamers cancorrespond to the two streamers situated at the outermost sides of a setcomprising a larger number of streamers.

[0080] The line Li forms part of an array (not shown) of lines coveringa zone Z (shown in the top of the figure) that is to be surveyed, saidarray constituting a “bin grid”.

[0081] The ship thus describes a set of lines that are generallyparallel to one another (all of the lines of the bin grid extending inthe same general direction), with the distance between two adjacentlines Li and Li+1 as shown in FIG. 2a being selected so as to obtain thedesired continuity of coverage between measurements of streamer S2 whenthe ship is passing along line Li and measurements of streamer S1 in thefollowing pass made by the same ship along line Li+1.

[0082] This desired continuity of coverage is represented in the topportion of FIG. 2a where different individual zones within the zone Z tobe covered are shown, said individual zones being covered by thestreamers of the ship 10 as it travels along the lines Li and Li+1.

[0083] Thus, while the ship was passing along the line Li the streamerscovered an individual zone Zi, and while the ship was passing along theline Li+1, the streamers covered an individual zone Zi+1. The twoindividual zones Zi and Zi+1 are contiguous.

[0084]FIG. 2a corresponds to an ideal configuration in which thestreamers extend parallel to the track of the ship and as a resultcoverage of the subsurface is uniform and sufficiently dense.

[0085] In FIG. 2b, it can be seen that unlike the case shown in FIG. 2a,the streamers do not have the same orientation relative to the shipduring the respective passes along lines Li and Li+1, the set ofstreamers being in alignment with the path of the ship only during itspass along line Li, whereas during the subsequent pass of the ship alongline Li+1, the portion of the streamers furthest from the ship is offsettransversely towards the line Li. This is typically due to the presenceof a current flowing across the lines Li and Li+1 while the ship ispassing along line Li+1.

[0086] Consequently, it can be seen in the top portion of FIG. 2b thatthe zone Z has been covered in part only, with an overlap zone Ri beinggenerated (which corresponds to “overcoverage”) while a portion Ii+1 ofthe zone Z is not properly covered during the pass of the ship alongline Li+1, and thus corresponds to a zone that is not actually covered(“undercoverage”).

[0087]FIG. 2c shows what happens when the change in current between twoconsecutive passes causes the zones covered by the sets of streamers todiverge during said two passes, thus leaving a zone I₀ of the subsurface(i.e. below the sea bed beneath the zone) that remains uncovered betweenthe two lines Li and Li+1.

[0088] It can thus be seen that depending on current configurations,there exist numerous possibilities for zones to be poorly covered (I₀,Ii+1). These zones represent areas that need to be filled in byadditional passes known as “infills”.

[0089] It will thus be understood that in operation, current conditionsoften give rise to such configurations, and certain regions can havecurrents that are strong and/or variable.

[0090]FIG. 3 thus constitutes an illustration of infills I provokedduring successive passes by changes in the orientation of the streamersS1 and S2 towed by a ship 10 (represented by a point traveling along itssuccessive path lines Li, Li+1, Li+2).

[0091] This figure (where the travel direction of the ship is indicatedby arrow F and where the scales of the X and Y axes corresponding to twohorizontal directions are not the same) also shows an area R ofovercoverage between adjacent passes Li and Li+1.

[0092]FIG. 2d shows the case where the streamers are subject to the samecross-current during two consecutive passes. The zone Z0 is covered atsufficient density in that said zone has been covered with streamergroups that are the furthest away from the ship on the first pass, andwith groups close to the ship on the second pass.

[0093] However, there can be seen a zone Zi that was insufficientlycovered during the first pass and a zone Zi+1 that was insufficientlycovered during the second pass.

[0094] A third pass with current identical to that of the first twopasses would enable the zone Zi+1 to be covered correctly by addingthereto coverage from the missing group, i.e. the near groups.

[0095] Successive identical passes for which the current is identical(so the streamers are parallel) thus make it possible, in application ofthe same principle, to cover an entire zone being surveyed, leaving onlytwo marginal zones with insufficient coverage.

[0096] A configuration of the type shown in FIG. 2 consequently providessatisfactory coverage of the subsurface.

[0097] As explained below, the invention makes use of this principle andenables the track to be followed by the ship on each pass to ensure thatthe orientation of the streamers during the pass is as closely parallelas possible to the orientation of the streamers during the pass alongthe previously acquired adjacent profile.

[0098] As mentioned, one means for predicting and reducing infills wouldbe to characterize the effect of current on streamer deformation in amanner that is realistic.

[0099] To this end, there follows a description of a method ofpredicting streamer orientation which, in a first aspect of theinvention, takes account of variations in current over time, and also ofvariations in speed and heading of the ship so as to replicate in amanner that is closer to reality the physical interactions betweencurrents and streamers.

[0100] General Principles

[0101] We begin by recalling certain fundamental characteristics ofmarine currents; it is known that currents encountered at sea are infact a superposition of a plurality of components:

[0102] tidal currents which are referred to as being “gravitational”:their ultimate origin is gravitational attraction; and

[0103] currents that are referred to as being “radiational”: their moreor less remote origin is solar radiation which is responsible forphenomena such as wind conditions, seasonal cycles, bad weather, orvariations of ocean density in three spatial dimensions that cangenerate movement within water masses. Radiational currents can besubdivided as follows:

[0104] a permanent component that is the result of the mean distributionof climate conditions over the surface of the globe;

[0105] a seasonal periodic component that is due to alternating seasons,which can be interpreted as cyclical modulation on the above-mentionedpermanent component; and

[0106] a non-periodic component originating from meteorological effects(weather currents).

[0107] By convention, the permanent and seasonal currents are referredto as general currents.

[0108] Tidal currents are deterministic and can be predicted over time.General currents are listed and can also be predicted. For example,tables of such currents are to be found in the pilot charts produced bythe United States National Oceanographic and Atmospheric Administration(NOAA) and in the Nautical Instructions published by the French MarineHydrographic and Oceanographic Service (SHOM).

[0109] In contrast, the currents generated by weather effects, which canto a first approximation be summarized as currents due to wind, arerandom. It is therefore advantageous to process them using statisticalmethods and it is shown below in the present description that theinvention provides an original method of predicting such currents and oftaking them into account where appropriate when predicting streamerdeformation.

[0110] It is also known that variations in the various currentcomponents do not all take place on the same time scales. Statisticalsurveys undertaken by the Applicant in various geographical zonesdistributed over different locations of the planet have shown thatdepending on the zone in consideration, the relative importance of thevarious current components can vary significantly.

[0111] Consequently, from one zone to another, the characteristics oftime variations in total currents are not the same, seasonal variationsbeing predominant in some zones whereas in other zones short-termvariability (due essentially to the wind) can be more significant, andyet other zones can have current conditions that are determined mainlyby general circulation so they are relatively stable, etc. . . .

[0112] As described in the specification below, the cable deformationprediction implemented in the invention cannot be summarized merely ascoupling a steady current model with a model for computing streamerdeformation as a function of given current conditions.

[0113] On the contrary, prediction also takes account of time aspectsassociated with marine current variations:

[0114] by making it possible as a function of the zone to be covered(and optionally also of the duration and the remoteness in time of theperiod over which geophysical data is to be acquired) to select thosecurrent components which will have a significant effect on timevariations in total current; and

[0115] by taking account of the variations due to said components.

[0116] The fact that the duration of the data acquisition period istaken into account is of importance particularly for applications of theinvention in the short or medium term. It is impossible to predictvariations in weather current over a period that is remote in time (i.e.starting a long time after the date at which prediction is made), oreven for a period that is too long.

[0117] That is why the method of the invention distinguishes betweencurrent components to be taken into account when predicting streamerdeformation by defining various “types” of current and by enabling auser to select a current “type” that is appropriate for requirements.

[0118] Beyond that, the invention also proposes making use of predicteddeformation in association with three different time horizons:

[0119] real time, during acquisition operations at sea. Here the purposeis to provide the ship with navigation assistance so as to continuouslyadjust the track of the ship so that at each instant the orientation ofthe streamers is as close as possible to their orientation at the samelevel (i.e. on the same position along the abscissa in the Y directionof FIG. 3) during the pass of the ship over the previously surveyedadjacent line, with this being for the purpose of reducing infills inreal time. This application is described more particularly in thepresent specification. To provide such navigation assistance, it isnecessary to have a prediction of current (at the depths correspondingto streamer immersion) for a time horizon whose order of magnitude is 1hour; the present specification also describes the characteristics of aprediction of current step that implements a current predictor (orshort-term prediction of current module);

[0120] medium term to determine, still during acquisition operations,the best path to be followed by the ship in order to survey thefollowing line. Thus, while the ship is traveling along a line Li, theobject of the method at this time scale (about 24 hours) is to determinethe best path for the ship to travel along the forthcoming adjacent lineLi+1, and also the most suitable time for beginning said line. It willbe observed that methods do indeed exist for performing such medium-termprediction. However, obtaining realistic results by predictions of tidalcurrent as implemented by those methods makes it necessary to haveaccurate bathymetric data at high three-dimensional resolution.Unfortunately, although that type of data is indeed sometimes available(e.g. SHOM data relating to French coastal zones), it is normally notavailable for zones that are to be surveyed. In any event, for thismedium-term time horizon, wind prediction models remain fairly randomand the predictions of the effects of wind on current are not reliable;

[0121] finally long term, under these circumstances the purpose is notto provide the ship with a track for reducing infills in operation, butto provide an overall prediction of the amount of infilling that will berequired due to a ship passing over a given zone, and possibly at agiven period (which period can be far in the future). This long-termprediction is then used to enable infills to be taken into account whenpredicting the cost and the duration of a projected operation.

[0122] Real-time and Medium-term Applications

[0123] Real-time and medium-term applications of the invention asimplemented on site are described below. These two types of applicationare implemented in a method of giving assistance in navigation that isassociated with the ship towing the streamers, said navigationassistance method using the predicted streamer deformations in real timeor in the medium term to give the ship an optimized track correspondingto minimizing infills (for the present profile or for the next profileto be shot, respectively). In any event, these applications areimplemented after the ship has already traveled along a first line.

Characteristics of the System Implemented by the Method for Real-timeand Medium-term Applications

[0124] As mentioned above, the Applicant has developed a system enablingthis navigation assistance method to be implemented. From the point ofview of the user, the system provides three main functions:

[0125] currents and streamer drift differences (streamer positions andorientations) are displayed. These parameters can be measured orpredicted (by a dedicated module whose characteristics are describedbelow in this specification insofar as they concern currents). On thisdisplay, comparing measured and predicted currents and drift differencesmakes it possible to judge the reliability of meteorological bulletins,of measurements of current, and of extrapolations made thereon;

[0126] defining and displaying the best next profile to shoot, i.e. theprofile for which the predicted drift of the streamers is closest to themeasured drift of an already-acquired adjacent profile at the same Yordinate position on the bin grid; and

[0127] defining and displaying in real time while a profile is beingrecorded the optimum track to be followed to avoid creating zones thatare undercovered or overcovered.

[0128] To perform these three functions, the system also implementsthree subassemblies as shown in FIG. 4:

[0129] a navigation software subassembly 51 which performs real-timeacquisition:

[0130] of the path of the ship (using conventional locating means, suchas means implementing one or more differential global positioning system(GPS) receivers);

[0131] of current data. This data can be in the form of measurementsfrom a current meter towed by the ship or on board the ship, or aspredicted on the basis of meteorological bulletins. This dataconstitutes “primary” data which is processed in the manner describedbelow in order to implement the invention; and

[0132] of the measured positions of the streamers, such measurementbeing performed by a suitable device (for this purpose, each streamer isfitted with a plurality of devices distributed along its length enablingits deformation to be measured and enabling the orientation of eachsegment of streamer having a device integrated therein to be determined,said devices implementing, for example, magnetic compasses, since onlythe horizontal components of current are taken into account);

[0133] a weather laboratory 52 which supplies predictions of current,wind, tide, and/or swell; and

[0134] a subassembly 53 for computing coverage and for display purposes,comprising:

[0135] a user interface such as a PC type or other computer providedwith a screen, a keyboard, and a mouse, together with means for storingdata; and

[0136] a module for defining, computing, and displaying various ‘currentobjects’ (defined below in this specification).

[0137] The subassemblies 51 and 53 are on board the ship 10 while theweather laboratory 52 can be separate from the ship. The data deliveredby the subassembly 51 is conveyed to the subassembly 53 via an Ethernettype link 54, for example, with data from the weather laboratory 52being conveyed to the same subassembly 53 over a wireless link 55, e.g.a link making use of the Internet and including a radio relay.

[0138] Data Received by the Navigation Software Subassembly 53

[0139] The subassembly 53 mainly receives four types of data from thesubassemblies 51 and 52:

[0140] meteorological bulletins and weather predictions supplied bydatabases;

[0141] measured current data acquired by means of the current meter;

[0142] streamer positioning data delivered by the measurement meansassociated with an acquisition and processing device; and

[0143] the path of the boat.

[0144] The characteristics of these four types of data are described ingreater detail below:

[0145] Weather Data

[0146] Weather predictions can come either from databases or frommeteorological bulletins received over the link 55.

[0147] Databases generally provide long-term predictions (severalmonths) of tidal currents; An example of the data format is as follows:Date of prediction Time of Height of waves due to tidal Normed tidalDirection of Decimal time of (GMT) prediction current (not used in thecurrent speed tidal current prediction (GMT) (dd/mm/yyy) (HH:MM) methodof the invention) (m) (m/s) (degrees) 0.00 Jan. 7, 1999 00:00 0.61 0.22171.7 0.10 Jan. 7, 1999 00:06 0.61 0.22 172.7 0.20 Jan. 7, 1999 00:120.62 0.22 173.7

[0148] Meteorological bulletins relating to prediction data at shorterterm (typically 36 hours) concerning currents, wind, or swell. Ingeneral, meteorological bulletins resolve the current vector into atidal current and a residual current. An example of the data format isas follows: Hours Wave height elapsed since due to Height of most recentresidual waves due to execution of current (not Normed Residual tidalcurrent bulletins used in the residual current (not used in Normed tidalTidal current generating method of the current speed direction themethod of current speed direction model invention) (m) (m/s) (degrees)the invention) (m/s) (degrees) 00 0.05 0.03 141.74 0.12 0.10 101.65 010.05 0.02 147.19 0.31 0.13 148.20 02 0.05 0.03 147.19 0.43 0.17 166.8003 0.05 0.03 149.74 0.45 0.18 177.00

[0149]  The frequency at which these bulletins are issued is of theorder of once or twice per day. The files are reformatted and ifnecessary processed and then stored in a database B associated withsubassembly 53. Although presently-available weather prediction servicescannot perform area sampling with resolution that is fine enough todistinguish a plurality of individual zones within most of the zonescovered by an acquisition operation, the system can take account of theprecise location of the point for which the weather prediction isperformed, in order to be able to take account of possible spatialvariations in weather data within a given coverage zone. Similarly, thesystem can take account of the depths of currents (to deduce predictionof current values by interpolation at the depths of the streamers whenthe predictions are given for a plurality of depths on either side ofstreamer depth).

[0150] In this specification, the term meteorological bulletin is usedboth for information coming from databases and for meteorologicalbulletins proper.

[0151] The database B stores general parameters (containing informationabout the body issuing the meteorological bulletin, the time and date ofthe bulletin, the dates and times of the beginning and end of theprediction, the type of data that has been predicted, and the format ofthe data), together with the data proper.

[0152] Two families of data are to be found in the weather data (thecurrent family and the swell family):

[0153] The data in the “current” family is characterized by a vectorwhose components (speed and the direction) vary with time, both for agiven location and for a given depth. This type of data is usable fortidal current meteorological bulletins, for residual current forecasts(which corresponds essentially to weather current), and to total currentand wind forecasts. Storage in the database B can be performed using thefollowing format: Longitude, latitude, depth (corresponding to ameasurement point), Date, time, speed (m/s), direction (degrees), Date,time, speed (m/s), direction (degrees), Etc. (a series of successivetime data items being stored in association with each measurementpoint), Longitude, latitude, depth (another measurement point), Date,time, speed (m/s), direction (degrees), Date, time, speed (m/s),direction (degrees), Etc.

[0154] Data of the “swell” family is derived from sea statemeteorological bulletins. The data in this family is created by a vectorwhose components (height, direction, and frequency) vary with time for agiven location. Storage in the database B can be in the followingformat: Longitude, latitude, date, time, height (m), period (s),direction (degrees), date, time, height (m), period (s), direction(degrees), etc. Longitude, latitude, date, time, height (m), period (s),direction (degrees), date, time, height (m), period (s), direction(degrees), etc.

[0155] Measured Current Data

[0156] This data comes from the on-board current meter (measuredcurrent) and is acquired in real time by the subassembly 51 and madeavailable to the subassembly 53 via a computer link referenced 54 inFIG. 4. This data is stored in the database B and is used withperiodicity lying in the range 1 minute (min) to 10 min. The structureof the data transferred over the link 54 is as follows:

[0157] Date, time, longitude, latitude,

[0158] Depth1 (m), speed (m/s), direction (degrees),

[0159] Depth2 (m), speed (m/s), direction (degrees),

[0160] Depth3 (m), speed (m/s), direction (degrees), Etc.

[0161] Streamer Group Drift

[0162] This data is computed in real time by the subassembly 51 and madeavailable to the subassembly 53 by the link 54.

[0163] During real-time acquisition of positioning data relating to aprofile (i.e. a line Li), the measured drift values are extracted andstored by the subassembly 53. Once the data has been imported by thesubassembly 53, the measured drift values are stored in the database B.

[0164] In order to determine the drift of the groups at each point wherethe sound source is fired, the entire system towed by the ship ismodelled as two virtual streamers S1 and S2 whose positions and shapescorrespond to a mean of the set of streamers in the system.

[0165] In the widespread case where the towed system in fact comprisesmore than two streamers, the two virtual streamers S1 and S2 aredescribed as follows:

[0166] for position, by the positions of the heads of the outermoststreamers of the system; and

[0167] for orientation by the mean of the shapes of the port streamers(for S1) and by the mean of the shapes of the starboard streamers (forS2).

[0168] More precisely, the shape of each streamer S1 and S2 is modelledby the position and orientation as measured in a horizontal planecomprising three streamer segments.

[0169] The structure of the data can be as follows:

[0170] Date, time, shot number, longitude, latitude, DXb, DYb (positionof the head of S1), φ1 b, φ2 b, φ3 b (orientations of three segments ofS1 relative to the Y direction or to north), DXt, DYt (position of thehead of S2), φ1 t, φ2 t, φ3 t (orientations of three segments of S2).

[0171] The Path of the Ship

[0172] The path of the ship is stored continuously at some definedrecurrence rate, in the following form:

[0173] Date, time, longitude, latitude, depth of water.

[0174] Definition of the Different “Current Types”

[0175] The subassembly 5″ has means for responding to the importedcurrent data (as measured or as predicted by meteorological bulletins)to define various types of current in a classification scheme devised bythe Applicant:

[0176] Type 1: measured current: this is the total current as measuredby a current meter;

[0177] Type 2: tidal current: this comes from meteorological bulletins,or is deduced from measurements of current by harmonic analysis;

[0178] Type 3: “tidal+weather lab residual” current: this is the sum ofa tidal current plus a residual current as supplied by a weatherforecasting body. The tidal current can come from meteorologicalbulletins, or it can be deduced from current meter measurements. Theresidual current comes form meteorological bulletins;

[0179] Type 4: “extrapolated future total” current: this is anextrapolation (performed by a specific predictor module integrated inthe subassembly 53, whose operation is described below, and which alsoserves to generate the extrapolated current values required forcomputing current “objects” of types 5, 6, and 7), of the total currentvector as measured by a current meter. Extrapolation of this current cancover the next three hours;

[0180] Type 5: “tidal+extrapolated future residual” current: this is thesum of a tidal current plus a residual current extrapolated by thepredictor as described below with reference to FIG. 6. The tidal currentcan come from meteorological bulletins or it can be deduced from currentmeter measurements. The extrapolated future residual current is computedby the predictor by extrapolating current meter measurements from whichtidal current has been subtracted. This current extrapolation can coverthe next 3 hours;

[0181] Type 6: “extrapolated past total” current: extrapolated pastcurrent corresponds to short-term predictions (the set of all 1-hourpredictions, for example) that the predictor has performed in the past.This is an extrapolation of one given term (e.g. 1 hour) of the totalcurrent vector as measured by a current meter. This current is computedbetween the beginning of the operation and the present instant;

[0182] Type 7: “tidal+extrapolated past residual” current: this is thesum of a tidal current plus a past residual current as extrapolated bythe predictor. The tidal current can come from meteorological bulletins,or it can be deduced from current meter measurements. The extrapolatedpast residual current corresponds to the short-term predictions (the setof all 1-hour predictions, for example) that the predictor has made inthe past. The extrapolated past residual current is computed byextrapolating measurements from a current meter that have had tidalcurrent values subtracted therefrom for one prediction term (1 hour inthis case). This current is computed between the beginning of theoperation and the present instant.

[0183] Definition of ‘Current Objects’ by the User

[0184] The computer of subassembly 53 is provided with interfacesoftware enabling the user to create a ‘current object’ which the systemis to process, by:

[0185] selecting a desired current type; and

[0186] giving specific parameters to the ‘current object’, whenevercreation of a ‘current object’ of a given type requires certainparameters to be selected.

[0187] To this end, the interface software displays a dialog box on thecomputer screen enabling the user:

[0188] to specify the selected current type. The user can select thistype as a function of the duration of the desired prediction period (ofhour order when assisting navigation in real time, of 24-hour order whenassisting towing of the next profile), and also as a function of thecharacteristics of the currents in the zone to be covered (predominanceof certain current components);

[0189] and also to create in the ‘current object’ system which isdefined not only by type, but also by the following parameters:

[0190] the name of the ‘current object’;

[0191] the names of the bodies issuing meteorological bulletins or ofthe current meters that the user wishes to select for tidal currents,residual currents, or other types of current;

[0192] the selected depth(s). The user can select any one of the currentmeters declared in the system; under such circumstances, “depth”information is defined by the first and the last cells between which theuser desires that the system should average current vectors;

[0193] for current types that involve past extrapolations: theprediction term; and

[0194] a graphical feature making it possible subsequently todistinguish on the screen of the interface the ‘current object’ asdefined in this way (a color or a symbol allocated to said ‘currentobject’, for example).

[0195] Depending on the type of the ‘current object’, all or only someof the above parameters need to be defined.

[0196] More precisely, in one implementation of the invention, inaddition to the name of the ‘current object’, its type, and twodetermined depths between which the user desires the vectorsrepresenting current to be averaged, and finally the graphical featureswhich the user desires to associate with the ‘current object’; the usermust also determine the parameters defined below for each respectivecurrent type: Current type number 1 2 3 4 5 6 7 Access path to data froma current meter X X X X X Current meter setting parameter(s) X X X X XAccess path to tidal current data X X X X Access path to residualcurrent data issued by a weather laboratory X Prediction term X X

[0197] The dialog box also enables the user to create, modify, delete,and duplicate these ‘current objects’ whose characteristics are storedin an associated memory location of the system.

[0198] Once the user has thus created a ‘current object’, it is possiblewhile operating over a zone to use the system to:

[0199] display variation over time in one or more desired ‘currentobjects’. To this end, the user informs the system of thecharacteristics that are to be displayed on the screen, as describedbelow. The system then computes values for the ‘current object’ eitherusing a time interval that can be assessed by the user, or else theoccurrence of a new event (new measurement of current, arrival of ameteorological bulletin, modification/deletion/creation of a ‘currentobject’ by the user, . . . );

[0200] display the streamer positioning differences (the position of astreamer being defined by the X, Y, Z positions of its points as afunction of time) by comparing simulated positions on the basis of‘current objects’ selected by the user and measured positions;

[0201] determining in real time the optimum track for the boat tofollow; and

[0202] optimizing the next profile to be shot by the boat.

[0203] For these four types of implementation, the system performsrecurrent computations on the ‘current object’ involved.

[0204] In the first two types of implementation measured above, thesystem always displays the way the measured values vary (type 1 ‘currentobject’ for the first implementation, difference between measuredposition and simulated position of a streamer as computed using a type 1‘current object’).

[0205] Such a simultaneous display of measured values enables the userto assess the quality of the various ‘current objects’ that have beendefined for display purposes and to select amongst them a ‘currentobject’ for one or other of the last two types of implementation.

[0206] In order to be able to compute ‘current objects’ based on primarycurrents issued by meteorological bulletins and/or the tidal currentdeduced from measurements of current over the zone, it is necessary tobegin by specifying the particular meteorological bulletins and/or theparticular tidal current file deduced from on-zone measurements ofcurrent. This is done by selecting:

[0207] for meteorological bulletins, the forecast whose reception timehas passed and which is the most recent to the instant for which aparticular value is to be computed for the ‘current object’; and

[0208] for tidal current files deduced from measurements of current, thefile whose creation date is past and is the most recent to the instantat which a particular value of the ‘current object’ is to be computed.

[0209] In addition, the way in which a ‘current object’ is computeddepends:

[0210] on the timing between the instant at which it is computed and therange of times for which it is computed; and

[0211] the type of implementation that needs it to be computed.

[0212] More precisely, three situations can arise:

[0213] the situation in which the instant at which the system performsthe computation of a ‘current object’ is after the time range for whichthe ‘current object’ is computed; in this case, the position of the shipas a function of time is known, and for each instant in the time base ofthe ‘current object’ interpolation is performed in space and in timebetween the current vectors of the primary current(s) used forconstructing the ‘current object’;

[0214] when the instant at which the system computes the ‘currentobject’ is earlier than the range of time for which the computation isperformed; in this case, the position of the ship as a function of timeis:

[0215] either unknown, for implementations of the type in whichvariation over time of ‘current object’ is displayed. In this case, thevalues of the ‘current object’ are computed by requiring the futureposition of the ship to be equal to the position of the ship at the timeat which the computation is performed. Interpolation in space istherefore the same for all of the instants in the time base of the‘current object’;

[0216] or else assumes, for implementations of the ‘real-timedetermination of optimum track’ and ‘optimization of next profile’types. This case reduces to the case mentioned above and for eachinstant in the time base of the ‘current object’, interpolation isperformed in space and in time between the current vectors of theprimary current(s) used for constructing the ‘current object’;

[0217] the case when the instant at which the system computes the‘current object’ lies within the range of times for which it iscomputed; in this case, two subranges of time are taken intoconsideration, one subrange being earlier than the instant at whichcomputation is performed and the other being subsequent to the instantof computation, and depending on which one of these two subrangescontains the instant for which a particular value of the ‘currentobject’ is computed, the computation reduces to one or other of the twokinds mentioned above.

[0218] Display of Currents and Drifts

[0219] This applies to the first two types of implementation of theinvention while operating on zones.

[0220] The interface of the subassembly 53 serves to display in the formof curves not only the track of the ship, but also the currents asmeasured and/or predicted, and the differences of streamer positioningas measured and as simulated. Comparing the measured and predictedvalues enables the user to assess in real time the quality of thepredictions, and possibly to select the most suitable ‘current object’if the present performance is judged to be inadequate.

[0221] Graphs of Predicted and Measured Currents

[0222] These graphs are representations of a plurality of curves thatare superposable as a function of time, together with a zoom option. Adialog box enables the user to create, modify, delete, and duplicatethese graphs. They are defined by:

[0223] the dates and times at the beginning and end of a graph;

[0224] a filter box for selecting the ‘current objects’ to be shown;

[0225] an ideal Y direction for the profiles;

[0226] the vector to be shown;

[0227] the ‘current objects’ to be used;

[0228] the projection of the speed of the current relative to thedefined direction;

[0229] the projection of the speed of the current relative to Xperpendicular to the defined Y direction; and

[0230] the same curves but after filtering has been applied thereto(sliding average, standard deviation, . . . ).

[0231] The graph is redrawn each time the system recomputes one of the‘current objects’ selected for the graph. The times on the graph arederived from the time differences applicable to current meteracquisition. A plurality of graphs can be shown simultaneously.

[0232] Graph of Differences and Drifts

[0233] The purpose of this graph is to show the lateral difference froma curvilinear abscissa of length 1000 m between the measured positionsof the streamers and a simulation of the positions of the streamersusing a ‘current object’ as selected by the user. The graph will be inthe form of a plurality of curves that are superposable as a function oftime with a zoom option. The graph can extend from the beginning ofoperations up to the present instant.

[0234] The user defines the graphs. A dialog box enables the user tocreate, modify, delete, and duplicate these graphs. They are defined by:

[0235] the dates and times at the beginning and the end of a graph; and

[0236] a filter box enabling ‘current objects’ to be selected for use incomputing simultaneous drifts, the object being selected from objects oftypes 1, 2, 3, 6, and 7.

[0237] The graph is redrawn after each profile. The time intervals ofthe graph are derived from the time differences of the profiles. Aplurality of graphs can be shown simultaneously.

[0238] Predictions of Current at Very Short Term

[0239] The system devised by the Applicant for implementing the methodof the invention comprises, as mentioned above, a short-term predictionof current module (which module is generally referred to as a“predictor”), that the system runs whenever it is necessary to compute a‘current object’ of type 4, 5, 6, or 7.

[0240] These short-term predictions are produced in real time and theyare used essentially for providing navigational assistance in real timeand for displaying ‘current objects’ and positioning differences betweena real streamer and a stimulated streamer. Predictor characteristics aredescribed below for the case where input data is in the form of valuesas measured for current up to the instant of prediction.

[0241] This linear predictor is required at an instant t to produce anestimate of the current at a future instant t+T0, on the basis solely ofa time series of current data measurements performed in situ up to theinstant t (e.g. by current meters previously moored in the zone or onboard the ship).

[0242] This predictor considers measured current data acquisition as asecond order non-centered steady random process. The predicted currentis the result of applying linear filtering to the available measureddata.

[0243] The components of the filter are deduced by solving a system oflinear equations that in turn is the result of minimizing errorvariation performed on the predicted value.

[0244] In outline, the predictor operates as follows:

[0245] Given measurement of current U(i) for i=1 to P, it is desired toproduce the best estimate of current Û(P+T0) from U up to the instantP+T0.

[0246] To do this, it is initially assumed that the current U is asecond order non-centered steady process, and the following notation isadopted: $U_{p} = {{\begin{pmatrix}{U(P)} \\{U\left( {P - 1} \right)} \\\vdots \\{U(1)}\end{pmatrix}\quad U_{P + {T0}}} = \begin{pmatrix}{U\left( {P + {T0}} \right)} \\{U(P)} \\{U\left( {P - 1} \right)} \\\vdots \\{U(1)}\end{pmatrix}}$

[0247] The estimate Û(P+T0) is the result of applying linear filteringto U_(p), i.e. is the scalar product of a vector C_(p) of dimension Pmultiplied by U_(p); Û(P + T0) = c_(P)^(T)U_(p)

[0248] Let e(P+T0) be the difference between U(P+T0) and its estimatedvalue Û(P+T0). The mathematical expectation can then be computed:$\begin{matrix}{{E\left\lbrack {e\left( {P + {T0}} \right)} \right\rbrack} = \quad {E\left\lbrack {{U\left( {P + {T0}} \right)} - {\hat{U}\left( {P + {T0}} \right)}} \right\rbrack}} \\{= \quad {E\left\lbrack {{U\left( {P + {T0}} \right)} - {c_{P}^{T}U_{p}}} \right\rbrack}} \\{= \quad {a^{T}{E\left\lbrack U_{P + {T0}} \right\rbrack}}}\end{matrix}$

[0249] In this computation, a vector a is used of dimension P+1, on theimplicit assumption that its first component is of value 1.

[0250] Estimation is based on the principle of minimizing error varianceunder the following constraints:

[0251] the mean error must be zero; and

[0252] the first component of the vector is equal to 1.

[0253] Mathematically, the parameters a1, a2, . . . , aP+1 aredetermined that minimize the relationship: $\begin{matrix}{G = \quad {E\left\lfloor \left( {{e\left( {P + {T0}} \right)} - {E\left\lbrack {e\left( {P + {T0}} \right)} \right\rbrack}} \right)^{2} \right\rfloor}} \\{= \quad {a^{T}\Gamma_{U}a}}\end{matrix}$

[0254] with the following constraints:

aE└U _(p+T0)┘=0  (1)

[0255] and

a 1=1  (2)

[0256] The matrix Γ_(u) is written: $\Gamma_{U} = \begin{pmatrix}\gamma_{0} & \gamma_{T\quad 0} & \gamma_{{T\quad 0} + 1} & \gamma_{{T\quad 0} + 1} & \cdots & \gamma_{P + {T\quad 0} - 1} \\\gamma_{T\quad 0} & \gamma_{0} & \gamma_{1} & \gamma_{2} & \cdots & \gamma_{P - 1} \\\gamma_{{T\quad 0} + 1} & \gamma_{1} & \gamma_{0} & \gamma_{1} & ⋰ & \vdots \\\gamma_{{T\quad 0} + 2} & \gamma_{2} & \gamma_{1} & \gamma_{0} & ⋰ & \gamma_{2} \\\vdots & \vdots & ⋰ & ⋰ & ⋰ & \gamma_{1} \\\gamma_{P + {T\quad 0} - 1} & \gamma_{P - 1} & \cdots & \gamma_{2} & \gamma_{1} & \lambda_{0}\end{pmatrix}$

[0257] γ_(i) being the autocovariance function of U.

[0258] U is assumed to be steady so its expectation does not vary overtime. Thus:${E\left\lfloor U_{p + {T\quad 0}} \right\rfloor} = {\begin{pmatrix}{\quad {E\left\lbrack {U\left( {P + {T0}} \right)} \right\rbrack}} \\{\quad {E\left\lbrack {U(P)} \right\rbrack}} \\{\quad {E\left\lbrack {U\left( {P - 1} \right)} \right\rbrack}} \\\vdots \\{\quad {E\left\lbrack {U(1)} \right\rbrack}}\end{pmatrix} = {{cte} \cdot \begin{pmatrix}1 \\1 \\1 \\\vdots \\1\end{pmatrix}}}$

[0259] Condition (2) thus becomes:${\sum\limits_{i = 1}^{P + 1}a_{i}} = 0$

[0260] and the problem then amounts to minimizing:$G = {\left( {1 - 1 - {\sum\limits_{i = 3}^{P + 1}{a_{i}a_{3}\quad \cdots \quad a_{p + 1}}}} \right){\Gamma_{U}\begin{pmatrix}1 \\{{- 1} - {\sum\limits_{i = 3}^{P + 1}a_{i}}} \\a_{3} \\\vdots \\a_{P + 1}\end{pmatrix}}}$

[0261] To minimize G, its gradient is said to be zero$\left( {\frac{\partial G}{\partial a_{i}} = {0\quad {\text{for~~all~~}\text{i}\text{~~in~~the~~range~~3~~to~~P+1}}}} \right),$

[0262] for all i in the range 3 to P+1), thus providing P−1 equations.After computation, the following system is obtained:

Amat_((P−1; P−1)) Usol=vect

[0263] where Amat_((p−1; p−1)) is symmetrical with Amat(i,j)=γ_(|j−i|)−γ_(j)−γ_(i)+γ₀

vect(i)=γ_(T0)−γ_(T0+1)+γ₁−γ₀

[0264] and

[0265] ${Usol} = \begin{pmatrix}a_{3} \\a_{4} \\\vdots \\a_{p + 1}\end{pmatrix}$

[0266] Solving the system of P-1 equations gives the vector a, whoselast P components are used for computing equation.

[0267] In practice, the function of the predictor is performed byexecuting a computer program. This program requires input in the form ofa measured current data series sampled at an interval dt.

[0268] After reading the values, the program performs prediction foreach time step nt=ndt. To do this, having the n preceding currentvalues, the program computes the statistical elements necessary forcomputing an autocorrelation function of these n values, andsubsequently for establishing the linear system of equations to besolved.

[0269] By solving the system, the program produces a prediction for thecurrent at nt+T0.

[0270] It should be observed that the number n of past measurements usedfor computing the autocorrelation function can be adjusted. The programalso gives weights to the n measurements of the input series that areinversely proportional to their age, so as to anticipate sudden changesdue to the residual current (corresponding to the weather current) whencomputing expectations necessary for obtaining the autocorrelationfunction.

[0271] In order to stabilize the predictions from the predictor andavoid deviant values, the Applicant has also implemented a method ofconditioning the linear system to be solved. In this respect, it isadvantageous to use a descent method and more particularly the conjugategradient method.

[0272]FIGS. 5a to 5 d show comparisons between measurements of currentand predictions P performed by the predictor module whose linear systemwas solved by a Gaussian method (FIGS. 5a and 5 c) and predictionsperformed by the conjugate gradient method (FIGS. 5b and 5 d). It can beseen that the deviant values produced by the Gaussian method disappearwhen using the conjugate gradient method. In addition this method turnsout to be beneficial in terms of computation time.

[0273] To evaluate the performance of the linear predictor, i.e. thedifference between the predicted current and the measured current (wherean acceptable error can be set at a value of about 2 centimeters persecond (cm/s) or even more), the Applicant has also made use of:

[0274] two main criteria:

[0275] the mean of the absolute value of the difference between theprediction and the measurement, written “abs error”; and

[0276] the difference between the prediction and the measurement belowthe value for which 90% of the prediction points are to be found; thisdifference is written “(90% difference)”;

[0277] the system also computes the average of the difference betweenthe prediction and the measurement in order to show up any possiblebias.

[0278] The table below shows 90% error and absolute error for predictionranges of 1 hour to 3 hours, the rows of the table corresponding todifferent conditions for performing in situ measurement of current.Thus:

[0279] the first three rows of the table correspond to the performanceof prediction performed on the basis of “S4” type current meters mooredat various different points B, E, L, and N in a zone, while row S4represents the mean of the performances in the first three rows; and

[0280] the row ADCP corresponds to performance relating to measurementscoming from an “acoustic Doppler current profiler” type instrument onboard a ship operating in the North Sea at a speed of 10 knots. 90%difference (cm/s) abs erreur (cm/s) Ranges 1 h 1.5 h 2 h 2.5 h 3 h 1 h1.5 h 2 h 2.5 h 3 h B 4.16 5.49 6.61 7.44 8.05 1.97 2.62 3.16 3.56 3.84E 8.52 11.07 13.11 14.60 15.59 3.99 5.20 6.21 6.89 7.32 L, N 5.29 7.088.71 10.06 11.04 2.51 3.38 4.19 4.86 5.35 S4 6.14 8.06 9.61 10.76 11.542.90 3.82 4.58 5.12 5.48 ADCP 8.97 13.81 17.92 21.71 24.62 3.82 6.098.13 9.81 11.14

[0281] It can be seen:

[0282] that for short-term prediction (to a horizon of about 1 hour andless) the absolute error is generally acceptable;

[0283] that there exists quite large disparity concerning the 90%difference criterion, and that its level is also higher; and

[0284] that the prediction performance when compared with ADCPmeasurement is significantly less good than when compared with currentmeters moored at fixed locations.

[0285] The Applicant has found that the errors that result fromcomparisons between predictions and ADCP measurements come essentiallyfrom the size of the very large geophysical zone covered by the shipassociated with the ADCP.

[0286] When taking measurements, the ship was traveling in coastal zonesand also in zones out at sea, and current conditions are different inthose two types of zone.

[0287] The performance of the predictor increases with implementation onsteady current conditions, in that a stable trend emerges over aplurality of consecutive measurement points.

[0288] The Applicant has thus integrated an improvement in the predictorfor showing up a harmonic portion in the in situ measured current, whichharmonic has easily predictable regular behavior, thus enabling thisharmonic portion to be subtracted from the total current and enablingthe linear predictor to be applied to the residual portion of thecurrent (i.e. the in situ measured current from which the harmonicportion has been subtracted).

[0289] It will be understood that, for example when a current has alarge tidal component, the residual amplitude must be significantlysmaller than that of the total current so that the prediction error asmeasured using the above-described criteria is decreased when comparedwith total current.

[0290] The general procedure of this processing is showndiagrammatically in FIG. 6. After in situ measurement of the currentbetween an instant nt0 in the past and an instant nt (step 701), aharmonic current is determined that is assumed to be the tidal current(step 702), and then at 703 this tidal current is subtracted from thetotal measured current in order at 704 to obtain a residual currentbetween the instants nt0 and nt (which current is by its very naturenon-harmonic).

[0291] Thereafter, this residual current is processed by the linearpredictor at 705 to produce a predicted residual current at a futureinstant nt+T0. Subsequently at 707, this predicted residual current isadded to the tidal current as predicted at 708 for instant nt+T0, wherethis prediction is deterministic. The result of this addition is used in709 as a prediction of the total current at nt+T0.

[0292] To obtain the harmonic tidal current, it is possible to use afinite element digital model based on a grid of the surveyed zone bysupplying limit conditions on the basis of the results of a larger scalemodel or of in situ measurements, or indeed by performing harmonicanalysis.

[0293] Such harmonic analysis can be performed by the procedure outlinedin FIG. 7. The process shown in this figure is analogous to thatdescribed above:

[0294] step 802 corresponds to computing the tidal current after aharmonic analysis step 801 in which the main tides contained in thecurrent measured at 800 are determined. This step leads to theequivalent of above-described step 702;

[0295] step 808 corresponds to above-described step 708. To predict thetidal current, tides are extrapolated (see below for an explanation ofhow tides are determined).

[0296] The Applicant has used such analysis on real current datacovering periods of 5 months for current meter B and 3 months forcurrent meter E.

[0297] To perform harmonic analysis, the system begins by applyingFourier analysis to the data series in order to identify peaks in thefrequency spectrum of the data that correspond to the main knowntide-generating waves (these waves being listed, for example, in thework “Introductory dynamical oceanography” by Pond and Pickard, wherethe main waves are semi-diurnal (waves M2, S2, N2, K2), diurnal (wavesK1, O1, P1, Q1) or of long period (Mf, Mn, Ssa)).

[0298] It is thus possible to extract the main harmonic components fromthe total current and the results of the procedure described withreference to FIGS. 6 and 7 are summarized in the table below, from whichit can be seen there is a very significant improvement in the quality ofprediction. 90% difference (cm/s) abs erreur (cm/s) Ranges 1 h 1.5 h 2 h1 h 1.5 h 2 h B 2.64 3.97 5.16 1.25 1.90 2.46 E 5.30 7.62 9.39 2.42 3.524.32

[0299] It will be understood that in operation it is necessary to have ahistory of measurements of current in order to be able to perform suchharmonic analysis which will also be performed on a periodic basis(about once per day).

[0300] In general, semi-diumal waves of type N2 are preponderant intidal harmonic components. In practice, it turns out that after the endof an initial on-site current measuring period of one to several days,the system has sufficient history to extract more significant harmoniccomponents from the measurements of current.

[0301] Optimizing the Track of the Ship In Real Time

[0302] There follows a description of the general principles and thestages in computing an optimum track for the ship in real time, thusconstituting the third type of implementation of the invention duringon-zone operations. This type of implementation makes use of analgorithm for seeking the optimum track.

[0303] In this case, the current data used is short-term prediction dataas selected by the user from above-defined types 2, 4, and 5 asdelivered by the above-described predictor module.

[0304] The purpose of this optimization is to provide the navigator atsome given repetition rate with an optimum track to follow, i.e. theoptimum position for the ship as a function of time, said optimum trackpossibly being provided directly by the subassembly 53 to the automaticpilot system of the ship.

[0305] On the basis of short-term predictions of current from thepredictor, and using the hydrodynamic cable deformation model, coverageoptimization amounts to finding the track to be given to the head of thestreamer, i.e. to the ship, so that future CMPs are offset by the widthof one cell in the X direction sideways from the preceding profile.

[0306] In a simplified version it can be assumed that the system (ship;streamer head) is not deformable. This assumption can be dropped byimplementing a hydrodynamic model that is capable of computing thedynamic deformations to which this system is subject, and to do so fastenough to be compatible with the algorithm for computing the optimumtrack as described below.

[0307] Navigation Algorithm

[0308] The navigation algorithm described below is used for thefollowing three applications of the invention: “real-time navigation”;“preparing the next profile”; and “preparation and study”.

[0309] In this part we begin by defining the following notation relatingto the adjacent profile (i.e. the profile for which data is known):

[0310] (Xa_(i,k), Ya_(i,k)) the coordinates of the various points of theouter streamer along the adjacent profile. Below, index “a” relates todata for the adjacent profile, index “i” relates to shot number, andindex “k” relates to the various points along a streamer (thecurvilinear abscissa constituted by the streamer being made discrete).By convention, k=1 corresponds to the head of the streamer and k=Kcorresponds to the tail of the streamer.

[0311] The following notation is defined relating to the referencestreamer (i.e. the “virtual” streamer which it is desired to match),with this streamer being obtained by shifting the streamer points of thepreceding profile by translation in the X direction while remaining atthe same level (same Y), and also possibly an associated set ofrotations all through an identical angle centered on the head of thestreamer at each shot point. In conventional manner, the translationcorresponds to an offset of one bin across the CMP line closest to theprofile to be optimized, but the method covers the possibility ofmodifying this distance. The angle of rotation is conventionally zero,but the method covers the possibility of including some other angle.

[0312] (Xc_(i,k), Yc_(i,k)) the coordinates of the various points alongthe reference streamer on the profile to be optimized. The index “c” isused below to mean “reference”.

[0313] The following notation is defined for the known parametersassociated with initial conditions of optimization. The initial instantcorresponds, for example, to the current instant when performingreal-time optimization, and to various acceptable instants for thebeginning of a profile when optimizing the next profile:

[0314] (X0 _(k), Y0 _(k)): the coordinates of the various points of thestreamer. In a “present profile” application, all of these points areknown, and they are transmitted to the system via the positioningmeasurement device. In a “next profile” application, only YO₁ is known(i.e. the Y component for the head of the streamer and the first shot onthe portion of track to be optimized). In this case, the shape of thestreamer is estimated by making assumptions concerning the speed of theship, and X0 ₁, becomes an unknown of the problem;

[0315] t0: the initial instant of the optimization.

[0316] The following notation is used for predictions of current:

[0317] (cx_(j,Ix,Iy,Iz), Cy_(j,Ix,Iy,Iz)): the components of the currentat instants subsequent to t0. Index “j” corresponds to the series ofinstants relating to predictions of current. The indices “Ix”, “Iy”,“Iz” correspond to the coordinates in three spatial dimensions of pointsof the ocean for which predictions of current are available.

[0318] The following notation is also defined relating to the optimumtrack:

[0319] (X1 _(i,k), Y1 _(i,k)): the coordinates of the various points ofthe outer streamer along the portion of profile being studied when theship follows the optimum track. The series Y1 _(i,1) (i.e. thesuccessive Y coordinates of the streamer head) is known and coincideswith the series Yc_(i,1). The series X1 _(i,1) (i.e. successive Xcoordinates of the streamer head) is an unknown of the problem. Theseries (X1 _(i,k), Y1 _(i,k)) for which “k” is different from 1 are theresult of the hydrodynamic model of streamer deformation;

[0320] t1 _(i) is the series of shot instants corresponding to theoptimum track. It is an unknown of the problem.

[0321] The following notation is also defined associated with weightingthe distance between the reference streamer and the streamer associatedwith the optimum track as a function of the curvilinear abscissa of thepoint under consideration of the streamer (“offset class”):

[0322] P_(k) is the weight to be associated to the difference betweenthe reference streamer and the streamer associated with the optimumtrack as a function of the offset class of the point of index “k” ineach of the two streamers.

[0323] The function to be minimized must be a norm of the differencebetween the reference streamer and the simulated streamer along theportion of profile that is to be optimized. By way of example, thisfunction can be expressed in the following various mathematical forms:${H\left( {{X1}_{i,1},{t1}_{i}} \right)} = {\sum\limits_{i = {i0}}^{I}{\sum\limits_{k = 1}^{K}{{{{Xc}_{i,k} - {X1}_{i,k}}}P_{k}}}}$${H\left( {{X1}_{i,1},{t1}_{i}} \right)} = {\sum\limits_{i = {i0}}^{I}{\sum\limits_{k = 1}^{K}{P_{k}\sqrt{\left( {{Xc}_{i,k} - {X1}_{i,k}} \right)^{2} + \left( {{Yc}_{i,k} - {Y1}_{i,k}} \right)^{2}}}}}$

[0324] i0 and I being respectively the numbers of the first and the lastfiring points on the track to be optimized.

[0325] Several methods can be envisaged for optimizing this function.There follows a description of one possible solving scheme based onseeking an optimum path in a graph. In contrast with the term “track”which designates a series of geographical points that vary in time, theterm “path” is used to designate a particular path through theoptimization graph. This particular solving scheme consists in:

[0326] initially defining a three-dimensional graph having twodimensions representing geographical coordinates and a third dimensionrepresenting time between two consecutive planes Y =Yn and Y=Yn+1;

[0327] simulating variation of the streamer as a function of all of thepaths that can be taken by the streamer head within the graph; and

[0328] selecting the track (X1 _(i,1), Y1 _(i,1), t1 _(i)) for which thefunction H(X1 _(i,1), t1 _(i)) is minimized.

[0329] Defining the Optimization Graph

[0330] We begin by defining the directions associated with the threedimensions of the graph. Thereafter, index “g” designates thecoordinates and the coordinate axes of the optimization graph. Thegeographical dimensions Xg and Yg of the graph are parallel to and inthe same direction as the corresponding axes X and Y used throughoutthis specification. Thus, in the optimization graph, Yg is parallel tothe general direction of the tracks followed by the ship, and Xg isperpendicular thereto. The time dimension ΔTg is a time difference orgoing from a plane Yg=Yg_(n) of the graph to the next following planeYg=Yg_(n+1).

[0331] The following notation is also defined, associated with thediscrete character of the three axes of the optimization graph:

[0332] ΔXg and ΔYg are the distances between two consecutive planes ofthe graph in the distances Xg and Yg respectively. ΔXg is anoptimization parameter to be entered by the user;

[0333] Δtg is the time step between two consecutive planes of the graphin the direction ΔTg; and

[0334] NXg, NYg, and NTg are the numbers of points of the graph in therespective directions Xg, Yg, and ΔTg.

[0335] The following notation is also defined relating to optimizationparameters to be defined by the user:

[0336] Vmin and Vmax are minimum and maximum speeds for the head of thestreamer;

[0337] φmax is the maximum difference between the heading of thestreamer head and the bearing of the ideal direction for the profiles;and

[0338] Xgmin, Xgmax are the minimum and maximum limits of the streamerhead along the Xg direction.

[0339] Using this notation, the following relationships apply:${\Delta \quad {Yg}} = \frac{\Delta \quad {Xg}}{\tan \left( {\phi \quad \max} \right)}$${\Delta \quad {Tg}_{1}} = \frac{\Delta \quad {Xg}}{{{\sin \left( {\phi \quad \max} \right)} \cdot V}\quad \max}$${\Delta \quad {Tg}_{NTg}} = \frac{\Delta \quad {Xg}}{{{\tan \left( {\phi \quad \max} \right)} \cdot V}\quad \min}$${\Delta \quad t\quad g} = \frac{{\Delta \quad {Tg}_{NTg}} - {\Delta \quad {Tg}_{1}}}{{NTg} - 1}$

[0340] The Yg axis of the graph has as its first point Yg₁ the pointwhich corresponds to the coordinate Yc_(i0,1) of the portion of profileto be optimized, and as its last point it has the point of coordinateYg_(NYg) such that Yg_(NYg)≦Yc_(I,1) and Yg_(NYg)+ΔYg>Yc_(I,1).

[0341] The Xg axis of the graph has as its first point Xg₁ the point ofcoordinate Xgmin entered by the user and as its lasts point the point ofcoordinate Xg_(NXg) such that Xg_(NYg)≦Xgmax and Xg_(NXg)+ΔYg>Xgmax.

[0342] The axis ΔTg of the graph has as its first and last points thepoints whose respective coordinates ΔTg₁ and ΔTg_(NTg) are given by theabove relationships.

[0343] In addition, notation relating to the projection of the referencestreamer coordinates (Xc_(i,k), Yc_(i,k)) on the optimization graph:

[0344] (Xcg_(ig,k), Ycg_(ig,k)) the coordinates of the various, pointsof the reference streamer along the profile to be optimized. The head ofthis “grid reference streamer” is included in the plane Yg=Yg_(ig). Itshould be observed that the coordinate Xcg_(ig,1) of the head of the“grid reference streamer” is almost certainly not included in the Xgplane of the optimization graph.

[0345] The projection of the reference points (Xc_(i,k), Yc_(i,k)) onthe optimization graph is performed by linear interpolation based on thetwo Yc coordinates of the reference streamer head of the shot pointsnumbered i and i+1 on either side of a plane Yg_(ig), i.e.:${Xcg}_{{ig},k} = \frac{\left( {{Yg}_{ig} - {Yc}_{i,1}} \right)\left( {{Xc}_{{i + 1},k} - {Xc}_{i,k}} \right)}{\left( {{Yc}_{{i + 1},1} - {Yc}_{i,1}} \right)}$${Ycg}_{{ig},k} = \frac{\left( {{Yg}_{ig} - {Yc}_{i,1}} \right)\left( {{Yc}_{{i + 1},k} - {Yc}_{i,k}} \right)}{\left( {{Yc}_{{i + 1},1} - {Yc}_{i,1}} \right)}$

[0346] The examples of the functions to be minimized as expressed abovein terms of coordinates relating to shot point number, are expressed interms of indices ixg and itg of the optimization grid as follows:${H\left( {{ixg}_{1},{{ixg}_{2,}\ldots}\quad,{ixg}_{NYg},{itg}_{1},{itg}_{2},\ldots \quad,{itg}_{NYg}} \right)} = {\sum\limits_{{ig} = 1}^{NYg}{\sum\limits_{k = 1}^{K}{{{{Xcg}_{{ig},k} - {X1g}_{{ig},k}}}P_{k}}}}$${H\left( {{ixg}_{1},{{ixg}_{2,}\ldots}\quad,{ixg}_{NYg},{itg}_{1},{itg}_{2},\ldots \quad,{itg}_{NYg}} \right)} = {\sum\limits_{{ig} = 1}^{NYg}{\sum\limits_{k = 1}^{K}{P_{k}\sqrt{\left( {{Xcg}_{{ig},k} - {X1g}_{{ig},k}} \right)^{2} + \left( {{Ycg}_{{ig},k} - {Y1g}_{{ig},k}} \right)^{2}}}}}$

[0347] Simulation of Streamer Variation as a Function of the DifferentPossible Paths and Selection of the Optimum Track

[0348] The possible paths within the above-defined optimization graphhave the following constraints:

[0349] the Y1g coordinate of the first point(s) of the path(s) is Yg₁;

[0350] in the “real-time track optimizing” application, the X1gcoordinate of the first path point is such that its ixg index minimizesthe distance |X1g₁−Xcg_(1,1)|;

[0351] in the “next profile” application, there are NXg starting pointscorresponding to the NXg point of the grid Xg; and

[0352] starting from a point having indices (ixg_(ig), itg_(ig)) in theplane Yg_(ig), it is possible to access points having indices(ixg_(ig+1), itg_(ig+1)) in the plane Yg_(ig+1), such that:ixg_(ig+1)=min(NXg, ixg_(ig)+1) or ixg_(ig+1)=ixg_(ig) orixg_(ig+1)=max(1, ixg_(ig)−1) and itg_(ig+1)=min(NTg, itg_(ig)+1) oritg_(ig+1)=itg_(ig) or itg_(ig+1)=max(1, itg_(ig)−1)

[0353] The graph is explored as follows:

[0354] an arbitrary “cost” (i.e. value of the function H to beminimized) of zero is given to the starting point(s), i.e. H_total(ixg₁,itg₁)=0;

[0355] all paths starting from a plane Yg_(ig) and going to thefollowing plane Yg_(ig+1) are simulated;

[0356] for all of these paths, an individual cost is computed, e.g.expressed as follows:${{H\_ uni}\left( {{ixg}_{ig},{{itg}_{ig};{ixg}_{{ig} + 1}},{itg}_{{ig} + 1}} \right)} = {\sum\limits_{k = 1}^{K}{{{{Xcg}_{{ig},k} - {X1g}_{{ig},k}}}P_{k}}}$

[0357]  for each arrival point in the plane Yg_(ig+1), the path isselected for which H_total(ixg_(ig), itg_(ig))+H_uni(ixg_(ig), itg_(ig);ixg_(ig+1), itg_(ig+1)) is a minimum, and this value is given toH_total(ixg_(ig+1), itg_(ig+1)); and

[0358] on reaching the last plane Yg_(NYg), the arrival point isselected which as the minimum value for H_total(ixg_(Nyg), itg_(NYg)).

[0359] Amongst other advantages, this method of exploring the graphpresents the following three major advantages:

[0360] since the number of possible paths has been made finite andcountable, a solution is indeed found and this solution is the optimumpath;

[0361] on reaching each new plane Yg_(ig+1), the method eliminates alarge number of potential paths (in application of the theorem whereby“every subtrack of an optimum track is optimum”), thus making the methodeasy to apply using present computer means for computation; and

[0362] the search for the optimum track is performed sequentially,thereby making it possible to stop computation at any moment and stillobtain a solution which is an optimum solution between the plane Yg₁ andthe plane Yg_(ig) at which computation was stopped.

[0363] Optimization of the Next Profile to be Surveyed by the Ship

[0364] This constitutes the fourth type of implementation of theinvention for on-zone operations.

[0365] During a mission, the next profile to be shot is determinedrelative to one of the profiles that has already been acquired and towhich the profile that is to be shot will be adjacent. The mainobjective in this second main application of the invention is todetermine the next profile and the time of the first shot of the soundsource for said profile so as to obtain streamer drift that is assimilar as possible to the drift in the adjacent profile.

[0366] The methods and computation modules described above for providingreal-time assistance in navigation are also implemented in thisoptimization. Nevertheless, medium-term application has features thatare specific thereto, since:

[0367] more time is available for computing the optimum track (theprediction term is now of half-day order);

[0368] however, since the term is more remote from the moment at whichprediction is performed, uncertainty is greater concerning current; and

[0369] finally, in this case the system is not content merely to computean optimum track portion, but must compute the optimum track along theentire length of the profile for each profile given by the user and foreach starting instant for which the user has defined the minimum andmaximum limits for each profile.

[0370] As mentioned above, in order to minimize infills, it is necessaryfor the streamer drifts to be parallel when passing through the same Yordinate on the optimization grid on two adjacent profiles. Theoptimization criterion is thus to minimize the weighted area between thestreamer of the adjacent profile that has already been carried out andthe shape of the streamer predicted for the next profile.

[0371]FIG. 11 illustrates this objective. In FIG. 11, the left-handportion shows two adjacent profiles 121 and 122 where it can be seenthat the streamers do not have the same orientation when passing throughthe same Y ordinate; this configuration is not optimum and it generatescoverage holes.

[0372] In the right-hand portion of the figure, the streamers S1 and S2are parallel for the profiles 123 and 124, with the profile 124 beingoptimized to provide a “best match” to the adjacent profile 123 whichhas already been carried out.

[0373] An optimization criterion is defined and is illustrated in FIG.12; it is computed for each plane Y=a constant in the optimization gridand it is proportional to the weighted area between the referencestreamer and the simulated streamer.

[0374] The sum of the individual areas for all of the points ofintersection between the head of the “reference” streamer and the planesY=a constant of the optimization grid of a profile to be shot iscomputed in such a manner as to evaluate the optimization ratio of agiven prediction.

[0375] Thus, for a given predicted profile, a value is available for anoptimization criterion that makes it possible to predict the quality ofthe coverage that ought to be associated with the profile.

[0376] For each profile given by the user and for each starting instantfor which the user has defined a time window in terms of minimum andmaximum limits, the program determines the optimum track and deducestherefrom the associated starting instant and optimization criterion.

[0377] The program makes it possible:

[0378] to select the candidate adjacent next profile and profile ends ifthe next profile does not have the same limits, in the Y direction forthe shot point as the adjacent profiles;

[0379] to select the ‘current object’ with which the predicted drift isto be computed (in this application, from objects of types 2 and 3);

[0380] to define a time window in which it is possible to begin the nextprofile (a utility in the subassembly 53 making it possible to selectone or more future profiles and to compute this information); and

[0381] to input general parameters and parameters relating toconfiguring the computation.

[0382] The program displays its results and stores them in memory. Foreach proposed profile and for each time for the first shot, storage willcomprise:

[0383] the value of the optimization criterion described with referenceto FIG. 12;

[0384] the optimum date and time for the first shot point;

[0385] the optimum speed and position of the boat at the first shotpoint; and

[0386] the number of shot points to which optimization applies comparedwith the number of shot points of the next profile.

[0387]FIG. 13 shows the appearance of the displayed results of variationin the optimization criterion as a function of time for three profiles141, 142, and 143.

[0388] The user also has the possibility:

[0389] of selecting a set {profile; starting time} and displaying itscharacteristics (value of the criterion; position and speed at the firstshot point; number of shot points used, . . . ); and

[0390] of selecting a set {profile: starting time} and then storing thetheoretical profile together with its drift for display on the coveragechart.

[0391] Long-term Application

[0392] The system described above can be implemented as mentioned inreal-time applications or medium-term applications for providingassistance in navigation for a ship. It can also be implemented in athird application of the invention for executing another method for thepurpose of predicting performance in terms of coverage associated with agiven bin grid prior to undertaking a projected acquisition operation.

[0393] For this type of application, the current data used relates tolong-term components of the current, i.e. to the tidal current and togeneral currents; in any event, the unsteady components of the current,i.e. components whose physical characteristics vary in the short term(typically the weather current that results in particular frominteraction with the wind) are excluded from this long-term application.

[0394] The idea here is to evaluate in advance performance in terms ofcoverage associated with a given zone (i.e. to evaluate rates ofundercoverage and overcoverage).

[0395] To perform such evaluation, the following can be made available:

[0396] an ideal acquisition direction;

[0397] a set of ideal rectilinear profiles;

[0398] geometrical and mechanical characteristics of the acquisitionapparatus; and

[0399] optionally the period during which it is proposed to perform dataacquisition.

[0400] Pertinent current measuring data is also available (tidal currentand general currents for the zone). In the absolute, and in the absenceof any specified acquisition period, the measured current data comprisesonly the above-mentioned long-term components of the current.

[0401] When an acquisition period is specified, other current componentsthat vary in the medium term can be taken into consideration if the timeinterval between the moment of evaluation and the beginning of theacquisition period is short.

[0402] As mentioned above, it is thus possible to evaluate performancein terms of coverage for a set of given ideal profiles by computing theoptimization criterion described with reference to FIG. 12 for said setof profiles.

[0403] In a variant of this method, it is also possible to use as inputdata the general orientation Y of the profiles to be shot, together withmeasured current data for the zone, and on the basis of a firstrectilinear ideal profile to implement a simulation that reproduces thecomputation steps described with reference to providing real-timeassistance in navigation so as to determine a set of paths that takeaccount of the mean measured current in the zone and that correspond toan optimized coverage fraction.

1. A method of simulating the positioning of a streamer towed by a ship(10) during an operation of acquiring geophysical data at sea, saidacquisition operation making use of shots from at least one sound source(Sa), the method implementing a hydrodynamic model of the interactionbetween marine current, the path of the ship, and the streamer, themethod being characterized in that it includes determining variations inthe current over time and in space.
 2. A method of simulating streamerpositioning according to claim 1, characterized in that the methodcomprises: receiving primary current values as measured and/orpredicted; defining vector fields or ‘current objects’ of respectivetypes corresponding to different representations of the current andbuilt up from said primary current values; and selecting a ‘currentobject’ as a function of the intended application.
 3. A method ofsimulating streamer positioning according to claim 2, characterized inthat ‘current object’ selection takes account of proximity in timebetween the instant for which the prediction is made and the instant atwhich prediction is performed.
 4. A method of simulating streamerpositioning according to claim 2 or 3, characterized in that ‘currentobject’ selection takes account of correlation between earlier ‘currentobject’ predictions and measurements of current performed at theinstants for which said earlier predictions were made.
 5. A method ofsimulating streamer positioning according to any one of claims 2 to 4,characterized in that the coordinates of at least some ‘current objects’comprise values measured on site.
 6. A method of simulating streamerpositioning according to any one of claims 2 to 5, characterized in thatthe coordinates of at least some ‘current objects’ comprise extrapolatedvalues predicting current.
 7. A method of simulating streamerpositioning according to claim 6, characterized in that some ‘currentobjects’ are computed by using a predictor filter enabling a currentdata series to be extrapolated from measurements of current made in theacquisition zone.
 8. A method of simulating streamer positioningaccording to claim 7, characterized in that the defined types of‘current object’ comprise the following types: 1) total current asmeasured by a current meter; 2) tidal current as derived frommeteorological bulletins, or as deduced from measurements of current byharmonic analysis; 3) the sum of a tidal current plus a residualcurrent, said tidal current being derived from meteorological bulletinsor being deduced from measurements of current by harmonic analysis, andsaid residual current being taken from meteorological bulletins; 4) anextrapolation from total current as measured by a current meter; 5) thesum of a tidal current and a computed residual current, said tidalcurrent being taken from meteorological bulletins or being deduced frommeasurements of current by harmonic analysis, and said residual currentbeing obtained by subtracting said tidal current from the currentmeasured in the acquisition zone; 6) a history of past extrapolations ofthe total current as measured by a current meter; and 7) the sum of atidal current and a history of past extrapolations of a series of valuesconstituted by the total current as measured by a current meter fromwhich a tidal current has been subtracted, said tidal current beingtaken from meteorological bulletins or being deduced from measurementsof current by harmonic analysis.
 9. A method of simulating streamerpositioning according to claim 8, characterized in that while computing‘current objects’ of types 4, 5, 6, or 7, the processed data series isconsidered as a second order non-centered steady random process.
 10. Amethod of simulating streamer positioning according to claim 8 or 9,characterized in that while computing values of a ‘current object’ oftype 4, 5, 6, or 7, weights are given to the measurements of the dataseries for extrapolation, which weights are inversely proportional totheir age, for the purpose of anticipating sudden changes due to theresidual current.
 11. A method of simulating streamer positioningaccording to any one of claims 8 to 10, characterized in that whilecomputing a particular value of a ‘current object’ of type 4, 5, 6, or7, a variance function of the difference between the predicted value andthe exact value of the current or the residual current at the instantfor which the prediction was computed is minimized, where said variancefunction has the form:$G = {\left( {1 - 1 - {\sum\limits_{i = 3}^{P + 1}{a_{i}\quad a_{3}\quad \ldots \quad a_{p + 1}}}} \right)\Gamma_{U}\quad \begin{pmatrix}1 \\{{- 1} - {\sum\limits_{i = 3}^{P + 1}a_{i}}} \\a_{3} \\\vdots \\a_{p + 1}\end{pmatrix}}$


12. A method of simulating streamer positioning according to any one ofclaims 8 to 11, characterized in that while computing a particular valueof a ‘current object’ of type 4, 5, 6, or 7, an autocorrelation functionof the current or residual current data series is computed, and then alinear system of equations is set up and solved.
 13. A method ofsimulating streamer positioning according to the preceding claim,characterized in that while computing a particular value of a ‘currentobject’ of type 4, 5, 6, or 7, the linear system to be solved isconditioned by implementing a descent method, preferably the conjugategradient method.
 14. A method of simulating streamer positioningaccording to any one of claims 7 to 13, characterized in that the methodprovides the option of computing extrapolated values on a series ofmeasured current values from which a tidal current has previously beensubtracted so as to compute an extrapolated residual current, and thenadding the tidal current corresponding to the instant for which theextrapolation has been made to said extrapolated residual current.
 15. Amethod of simulating streamer positioning according to any one of claims6 to 14, characterized in that the method comprises estimating theperformance of different predictions of current by comparison with ameasurement of current performed at the time corresponding to the timeof the predictions.
 16. A method of simulating streamer positioningaccording to any one of claims 6 to 15, characterized in that the methodcomprising estimating the performance of a ‘current object’ derived frompredictions and/or measurements of current by comparing the measuredstreamer positioning and the simulated streamer positioning, saidsimulation taking account of the ‘current object’ whose performance isto be estimated.
 17. A method of simulating streamer positioningaccording to the preceding claim, characterized in that the performanceof the ‘current object’ is described by criteria which comprise theaverage of the absolute value of the difference between measurement andsimulation of streamer positioning, and/or the difference betweenpredicted and measured streamer positioning below the value for which90% of the prediction points are to be found.
 18. A method of assistingthe navigation of a ship towing at least one streamer in order to reducezones of undercoverage and/or overcoverage generated during ageophysical data acquisition operation at sea during which the shiptravels along a plurality of lines (Li, Li+1, Li+2) extending in ageneral Y direction defining an abscissa and forming an array covering adesired zone, the method being characterized in that it implements amethod of simulating streamer positioning according to any precedingclaim.
 19. A method of assisting navigation according to the precedingclaim, the ship having already traveled along one of the lines of saidarray, the method being characterized in that it comprises determiningthe set of {ship position; instant} pairs at regular intervals in spaceso as to define a track along which the orientation of the streamer(9210) at a given abscissa along the general orientation of the lines ofthe array is as close as possible to the orientation of an associatedstreamer (9200) during a previous pass of the ship along an adjacentline.
 20. A method of assisting navigation according to claim 18 or 19,characterized in that the method comprises the following steps:selecting a ‘current object’ of appropriate type; defining optimizationparameters; computing the positioning of a ‘reference streamer’ fromdata relating to the streamer positioning of the adjacent profile andthe optimization parameters; taking account of ship speed and directiondata and streamer positioning data at the time optimization computationis started; creating a three-dimensional optimization grid with a firstdimension (Y) parallel to said general direction, a second direction (X)being perpendicular to the general direction, and included in thehorizontal plane, and the third dimension (DT) representing possibletime increments between two nodes spaced apart by one grid cell in thegeneral direction (Y); simulating variations in the positioning of thestreamer towed by a ship following all of the tracks defined by thenodes of the optimization grid; for all of the possible tracks,computing a norm of the difference between simulated streamerpositioning and reference streamer positioning; and computing an optimumtrack for which the associated norm is a minimum.
 21. A method ofassisting navigation according to the preceding claim, characterized inthat the optimization step comprises minimizing a norm of the differencebetween reference streamer positioning and simulated streamerpositioning.
 22. A method of assisting navigation according to thepreceding claim, characterized in that said normal to be minimized hasthe form:${H\left( {{X1},{\delta \quad {t1}}} \right)} = {\sum\limits_{j = 1}^{J}{\sum\limits_{k = 1}^{K}{{{{X_{refernce}\left( {k,j} \right)} - {X_{predicted}\left( {k,j} \right)}}}{f(k)}}}}$

where: X1 is a series of J consecutive values for the position of thestreamer head along the horizontal direction of the optimization gridperpendicular to the general direction; δt1 is a series of J consecutivevalues for the duration taken by the streamer head to pass form one nodeof the optimization grid of coordinates (X_(i1), Y_(j), δt_(k1)) to anode having coordinates (X_(i2), Y_(j+1), δt_(k2)); J is the number ofnodes of the grid in said general direction (Y); K is the number ofcurvilinear abscissa points along the discretized streamer;X_(reference)(k, j) is the position along the X axis of the point “k” ofthe ‘reference streamer’ when the head thereof is at the jth plane ofthe optimization grid along the Y axis; X_(predicted)(k, j) is theposition along the X axis of the point “k” of the simulated streamerwhen the head thereof is at the jth plane of the optimization grid alongthe Y axis; and f(k) is a weighting function applied to the differencebetween the simulated streamer and the reference streamer.
 23. A methodof assisting navigation according to claim 21 or claim 22, characterizedin that the method implements an optimization criterion for saiddifference between the measured and predicted streamer-positioning data.24. A method of assisting navigation according to any one of claims 19to 23, characterized in that the step of optimizing zone coverage isimplemented in real time so as to provide the ship with a series of{instant; ship position; ship speed} triplets to follow so as tooptimize the path of the ship along a line that the ship is surveying.25. An application of the method of assisting navigation according toany one of claims 19 to 23 to determining a path and a starting timeassociated with a forthcoming line that is to be surveyed by the ship,and also for determining the best forthcoming line to survey.
 26. Anapplication according to the preceding claim, characterized in that aline starting time is sought from within a given time window thatcorresponds to minimizing undercoverage and overcoverage.
 27. A methodof predicting the coverage fraction associated with an operation ofacquiring geophysical data that is to be performed at sea over a givenzone, the method being characterized in that it implements simulatingthe track of a ship including a method of assisting navigation accordingto any one of claims 18 to 23.